A179108 - OEIS

%I #24 Oct 13 2023 06:50:01

%S 2,46,109,5234,8158,720114,28187351,110781386,154319269,384242766,

%T 390620082,3790689201,65589428378

%N Values x for records of minima of positive distance d between a square cubefree integer y and a cube of positive and squarefree integer x and such d = y^2 - x^3.

%C If x=n^2 and y=n^3 distance d=0.

%C For d values see A179107.

%C For y values see A179109.

%C For numbers x from 46 to 108 distance can't be less than 8.

%C For numbers x from 109 to 5233 distance can't be less than 15.

%C For numbers x from 5234 to 8157 distance can't be less than 17.

%C For numbers x from 8158 to 729113 distance can't be less than 24.

%C For numbers x from 729114 to 28187350 distance can't be less than 225.

%C Next conjectured terms are: 53197086958290, 12813608766102800, 810574762403977000, 471477085999389000.

%t d = 3; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)] + 1; k = m^2 - n^d; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 720114}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; xx (* _Artur Jasinski_, Oct 30 2011 *)

%Y Cf. A179107, A179109.

%Y Cf. A078933. [From _R. J. Mathar_, Oct 13 2010]

%K more,nonn

%O 1,1

%A _Artur Jasinski_, Jun 29 2010